Problem: You are given an integer N.

Construct any one N-by-N matrix a that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.

* 1 \leq a_{i,j} \leq 10^{15}
* a_{i,j} are pairwise distinct integers.
* There exists a positive integer m such that the following holds: Let x and y be two elements of the matrix that are vertically or horizontally adjacent. Then, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always m.

Constraints

* 2 \leq N \leq 500

Input

Input is given from Standard Input in the following format:


N


Output

Print your solution in the following format:


a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Output

Print your solution in the following format:


a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Example

Input

2


Output

4 7
23 10

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 29);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            DModuloMatrix solver = new DModuloMatrix();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DModuloMatrix {
        Debug debug = new Debug(false);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = 504;//in.readInt();
            long[][] mat = new long[n][n];
            EulerSieve sieve = new EulerSieve(10000);
            int[] row = new int[n];
            int[] col = new int[n];
            for (int i = 0; i < n / 2; i++) {
                row[i] = sieve.get(i * 2 + 3);
                col[i] = sieve.get(i * 2 + 4);
            }

            row = zigzag(row, 0, n / 2 - 1);
            col = zigzag(col, 0, n / 2 - 1);

            debug.debug("row", row);
            debug.debug("col", col);

            int[] expandRow = new int[n];
            int[] expandCol = new int[n];
            for (int i = 0; i < n; i += 2) {
                expandRow[i] = row[i / 2];
                expandRow[i + 1] = 2 * row[i / 2];
                expandCol[i] = col[i / 2];
                expandCol[i + 1] = 3 * col[i / 2];
            }
            debug.debug("expandRow", expandRow);
            debug.debug("expandCol", expandCol);

            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if ((i + j) % 2 == 0) {
                        mat[i][j] = expandRow[i] * expandCol[j];
                    }
                }
            }

            int[][] dirs = new int[][]{
                    {-1, 0},
                    {1, 0},
                    {0, -1},
                    {0, 1}
            };
            for (int i = 1; i < n - 1; i++) {
                for (int j = 1; j < n - 1; j++) {
                    if ((i + j) % 2 == 0) {
                        continue;
                    }
                    long lcm = 1;
                    for (int[] dir : dirs) {
                        int x = i + dir[0];
                        int y = j + dir[1];
                        if (x < 0 || y < 0 || x >= n || y >= n) {
                            continue;
                        }
                        lcm = LCMs.lcm(lcm, mat[x][y]);
                    }
                    if (i % 2 == 0) {
                        lcm *= 2;
                    }
                    mat[i][j] = lcm + 1;
                }
            }

            int m = in.readInt();
            for (int i = 1; i <= m; i++) {
                for (int j = 1; j <= m; j++) {
                    out.append(mat[i][j]).append(' ');
                }
                out.println();
            }
        }

        public int[] zigzag(int[] data, int l, int r) {
            int[] ans = new int[data.length];
            int offset = 0;
            while (l <= r) {
                ans[offset++] = data[l];
                if (r >= l + 1) {
                    ans[offset++] = data[r];
                }
                l++;
                r--;
            }
            return ans;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            return this;
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class EulerSieve {
        private int[] primes;
        private boolean[] isComp;
        private int primeLength;

        public int get(int k) {
            return primes[k];
        }

        public EulerSieve(int limit) {
            isComp = new boolean[limit + 1];
            primes = new int[limit + 1];
            primeLength = 0;
            for (int i = 2; i <= limit; i++) {
                if (!isComp[i]) {
                    primes[primeLength++] = i;
                }
                for (int j = 0, until = limit / i; j < primeLength && primes[j] <= until; j++) {
                    int pi = primes[j] * i;
                    isComp[pi] = true;
                    if (i % primes[j] == 0) {
                        break;
                    }
                }
            }
        }

    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;
        static int[] empty = new int[0];

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, Object x) {
            return debug(name, x, empty);
        }

        public Debug debug(String name, Object x, int... indexes) {
            if (offline) {
                if (x == null || !x.getClass().isArray()) {
                    out.append(name);
                    for (int i : indexes) {
                        out.printf("[%d]", i);
                    }
                    out.append("=").append("" + x);
                    out.println();
                } else {
                    indexes = Arrays.copyOf(indexes, indexes.length + 1);
                    if (x instanceof byte[]) {
                        byte[] arr = (byte[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof short[]) {
                        short[] arr = (short[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof boolean[]) {
                        boolean[] arr = (boolean[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof char[]) {
                        char[] arr = (char[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof int[]) {
                        int[] arr = (int[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof float[]) {
                        float[] arr = (float[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof double[]) {
                        double[] arr = (double[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else if (x instanceof long[]) {
                        long[] arr = (long[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    } else {
                        Object[] arr = (Object[]) x;
                        for (int i = 0; i < arr.length; i++) {
                            indexes[indexes.length - 1] = i;
                            debug(name, arr[i], indexes);
                        }
                    }
                }
            }
            return this;
        }

    }

    static class GCDs {
        private GCDs() {
        }

        public static long gcd(long a, long b) {
            return a >= b ? gcd0(a, b) : gcd0(b, a);
        }

        private static long gcd0(long a, long b) {
            return b == 0 ? a : gcd0(b, a % b);
        }

    }

    static class LCMs {
        private LCMs() {
        }

        public static long lcm(long x, long y) {
            return x / GCDs.gcd(x, y) * y;
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }
}